Barrera, J., Homem-De-Mello, T., Moreno, E., Pagnoncelli, B. K., & Canessa, G. (2016). Chance-constrained problems and rare events: an importance sampling approach. Math. Program., 157(1), 153–189.
Abstract: We study chance-constrained problems in which the constraints involve the probability of a rare event. We discuss the relevance of such problems and show that the existing sampling-based algorithms cannot be applied directly in this case, since they require an impractical number of samples to yield reasonable solutions. We argue that importance sampling (IS) techniques, combined with a Sample Average Approximation (SAA) approach, can be effectively used in such situations, provided that variance can be reduced uniformly with respect to the decision variables. We give sufficient conditions to obtain such uniform variance reduction, and prove asymptotic convergence of the combined SAA-IS approach. As it often happens with IS techniques, the practical performance of the proposed approach relies on exploiting the structure of the problem under study; in our case, we work with a telecommunications problem with Bernoulli input distributions, and show how variance can be reduced uniformly over a suitable approximation of the feasibility set by choosing proper parameters for the IS distributions. Although some of the results are specific to this problem, we are able to draw general insights that can be useful for other classes of problems. We present numerical results to illustrate our findings.
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Beltran, J. F., Nunez, E., Nunez, F., Silva, I., Bravo, T., & Moffat, R. (2018). Static response of asymmetrically damaged metallic strands: Experimental and numerical approach. Constr. Build. Mater., 192, 538–554.
Abstract: In this study, the effect of the presence of broken wires (damage) asymmetrically distributed on metallic strands surfaces on their static response is assessed. To this end, a general mechanical model for multi layered strands is presented, in which damaged strands are treated as a 1D nonlinear beam under uncoupled biaxial bending and axial load (NLBM). The NLBM is validated by comparisons with the results obtained from an experimental program especially designed for studying the effect of surface damage distribution on strands response and 3D nonlinear finite element simulations. Analyses are carried out on two strand constructions: 1 x 7 and 1 x 19, in which the damage levels and strand diameters vary from 5% to 40% and from 3.5 mm to 22.2 mm, respectively. Results indicate that the NLBM accurate predicts the static response (residual strength, stiffness, axial strain field, and deformed configuration) of the asymmetrically damaged strands, achieving good computational efficiency and numerical robustness. (C) 2018 Elsevier Ltd. All rights reserved.
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Bustos, C., Herrera, C. G., Celentano, D., Chen, D. M., & Cruchaga, M. (2016). Numerical Simulation and Experimental Validation of the Inflation Test of Latex Balloons. Lat. Am. J. Solids Struct., 13(14), 2357–2378.
Abstract: Experiments and modeling aimed at assessing the mechanical response of latex balloons in the inflation test are presented. To this end, the hyperelastic Yeoh material model is firstly characterized via tensile test and, then, used to numerically simulate via finite elements the stress-strain evolution during the inflation test. The numerical pressure-displacement curves are validated with those obtained experimentally. Moreover, this analysis is extended to a biomedical problem of an eyeball under glaucoma conditions.
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Castaneda, P., & Reus, L. (2019). Suboptimal investment behavior and welfare costs: A simulation based approach. Financ. Res. Lett., 30, 170–180.
Abstract: We propose a representation of suboptimal investment behavior based on the stochastic discount factor (SDF) paradigm. Suboptimal investment behavior is rationalized as being the investor's optimal decision under a wrong SDF, while wealth trajectories and budget constraints are based on the true SDF. We develop a novel Monte Carlo simulation approach to compute the welfare costs for this suboptimal behavior. We study the suboptimal portfolio choice under CRRA preferences using two financial market models. The Monte Carlo simulation delivers comparable welfare losses to those computed in the original studies, which are based on partial differential equations (PDE) and – finite-difference schemes.
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Comisso, L., & Asenjo, F. A. (2021). Magnetic reconnection as a mechanism for energy extraction from rotating black holes. Phys. Rev. D., 103(2), 023014.
Abstract: Spinning black holes store rotational energy that can be extracted. When a black hole is immersed in an externally supplied magnetic field, reconnection of magnetic field lines within the ergosphere can generate negative energy (relative to infinity) particles that fall into the black hole event horizon while the other accelerated particles escape stealing energy from the black hole. We show analytically that energy extraction via magnetic reconnection is possible when the black hole spin is high (dimensionless spin a similar to 1) and the plasma is strongly magnetized (plasma magnetization sigma(0) > 1/3). The parameter space region where energy extraction is allowed depends on the plasma magnetization and the orientation of the reconnecting magnetic field lines. For sigma(0) >> 1, the asymptotic negative energy at infinity per enthalpy of the decelerated plasma that is swallowed by a maximally rotating black hole is found to be epsilon(infinity)(-) similar or equal to – root sigma(0)/3. The accelerated plasma that escapes to infinity and takes away black hole energy asymptotes the energy at infinity per enthalpy epsilon(infinity)(+) similar or equal to root 3 sigma(0).. We show that the maximum power extracted from the black hole by the escaping plasma is P-extr(max) similar to 0.1M(2) root sigma(0)w(0) (here, M is the black hole mass and w(0) is the plasma enthalpy density) for the collisionless plasma regime and one order of magnitude lower for the collisional regime. Energy extraction causes a significant spindown of the black hole when a similar to 1. The maximum efficiency of the plasma energization process via magnetic reconnection in the ergosphere is found to be eta(max) similar or equal to 3/2. Since fast magnetic reconnection in the ergosphere should occur intermittently in the scenario proposed here, the associated emission within a few gravitational radii from the black hole is expected to display a bursty nature.
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Cortes, C. E., Jara-Moroni, P., Moreno, E., & Pineda, C. (2013). Stochastic transit equilibrium. Transp. Res. Pt. B-Methodol., 51, 29–44.
Abstract: We present a transit equilibrium model in which boarding decisions are stochastic. The model incorporates congestion, reflected in higher waiting times at bus stops and increasing in-vehicle travel time. The stochastic behavior of passengers is introduced through a probability for passengers to choose boarding a specific bus of a certain service. The modeling approach generates a stochastic common-lines problem, in which every line has a chance to be chosen by each passenger. The formulation is a generalization of deterministic transit assignment models where passengers are assumed to travel according to shortest hyperpaths. We prove existence of equilibrium in the simplified case of parallel lines (stochastic common-lines problem) and provide a formulation for a more general network problem (stochastic transit equilibrium). The resulting waiting time and network load expressions are validated through simulation. An algorithm to solve the general stochastic transit equilibrium is proposed and applied to a sample network; the algorithm works well and generates consistent results when considering the stochastic nature of the decisions, which motivates the implementation of the methodology on a real-size network case as the next step of this research. (C) 2013 Elsevier Ltd. All rights reserved.
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de la Cruz, R., Salinas, H. S., & Meza, C. (2022). Reliability Estimation for Stress-Strength Model Based on Unit-Half-Normal Distribution. Symmetry, 14(4), 837.
Abstract: Many lifetime distribution models have successfully served as population models for risk analysis and reliability mechanisms. We propose a novel estimation procedure of stress-strength reliability in the case of two independent unit-half-normal distributions can fit asymmetrical data with either positive or negative skew, with different shape parameters. We obtain the maximum likelihood estimator of the reliability, its asymptotic distribution, and exact and asymptotic confidence intervals. In addition, confidence intervals of model parameters are constructed by using bootstrap techniques. We study the performance of the estimators based on Monte Carlo simulations, the mean squared error, average bias and length, and coverage probabilities. Finally, we apply the proposed reliability model in data analysis of burr measurements on the iron sheets.
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During, G., Josserand, C., & Rica, S. (2017). Wave turbulence theory of elastic plates. Physica D, 347, 42–73.
Abstract: This article presents the complete study of the long-time evolution of random waves of a vibrating thin elastic plate in the limit of small plate deformation so that modes of oscillations interact weakly. According to the wave turbulence theory a nonlinear wave system evolves in longtime creating a slow redistribution of the spectral energy from one mode to another. We derive step by step, following the method of cumulants expansion and multiscale asymptotic perturbations, the kinetic equation for the second order cumulants as well as the second and fourth order renormalization of the dispersion relation of the waves. We characterize the non-equilibrium evolution to an equilibrium wave spectrum, which happens to be the well known Rayleigh-Jeans distribution. Moreover we show the existence of an energy cascade, often called the Kolmogorov-Zakharov spectrum, which happens to be not simply a power law, but a logarithmic correction to the Rayleigh Jeans distribution. We perform numerical simulations confirming these scenarii, namely the equilibrium relaxation for closed systems and the existence of an energy cascade wave spectrum. Both show a good agreement between theoretical predictions and numerics. We show also some other relevant features of vibrating elastic plates, such as the existence of a self-similar wave action inverse cascade which happens to blow-up in finite time. We discuss the mechanism of the wave breakdown phenomena in elastic plates as well as the limit of strong turbulence which arises as the thickness of the plate vanishes. Finally, we discuss the role of dissipation and the connection with experiments, and the generalization of the wave turbulence theory to elastic shells. (C) 2017 Elsevier B.V. All rights reserved.
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Fierro, R., & Leiva, V. (2017). A stochastic methodology for risk assessment of a large earthquake when a long time has elapsed. Stoch. Environ. Res. Risk Assess., 31(9), 2327–2336.
Abstract: We propose a stochastic methodology for risk assessment of a large earthquake when a long time has elapsed from the last large seismic event. We state an approximate probability distribution for the occurrence time of the next large earthquake, by knowing that the last large seismic event occurred a long time ago. We prove that, under reasonable conditions, such a distribution is exponential with a rate depending on the asymptotic slope of the cumulative intensity function corresponding to a nonhomogeneous Poisson process. As it is not possible to obtain an empirical cumulative distribution function of the waiting time for the next large earthquake, an estimator of its cumulative distribution function based on existing data is derived. We conduct a simulation study for detecting scenario in which the proposed methodology would perform well. Finally, a real-world data analysis is carried out to illustrate its potential applications, including a homogeneity test for the times between earthquakes.
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Fustos-Toribio, I., Manque-Roa, N., Vasquez Antipan, D., Hermosilla Sotomayor, M., & Gonzalez, V. L. (2022). Rainfall-induced landslide early warning system based on corrected mesoscale numerical models: an application for the southern Andes. Nat. Hazards Earth Syst. Sci., 22(6), 2169–2183.
Abstract: Rainfall-induced landslides (RILs) are an issue in the southern Andes nowadays. RILs cause loss of life and damage to critical infrastructure. Rainfall-induced landslide early warning systems (RILEWSs) can reduce and mitigate economic and social damages related to RIL events. The southern Andes do not have an operational-scale RILEWS yet. In this contribution, we present a pre-operational RILEWS based on the Weather and Research Forecast (WRF) model and geomorphological features coupled to logistic models in the southern Andes. The models have been forced using precipitation simulations. We correct the precipitation derived from WRF using 12 weather stations through a bias correction approach. The models were trained using 57 well-characterized RILs and validated by ROC analysis. We show that WRF has strong limitations in representing the spatial variability in the precipitation. Therefore, accurate precipitation needs a bias correction in the study zone. We used accurate precipitation simulation and slope, demonstrating a high predicting capacity (area under the curve, AUC, of 0.80). We conclude that our proposal could be suitable at an operational level under determined conditions. A reliable RIL database and operational weather networks that allow real-time correction of the mesoscale model in the implemented zone are needed. The RILEWSs could become a support to decision-makers during extreme-precipitation events related to climate change in the south of the Andes.
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Garcia-Papani, F., Uribe-Opazo, M. A., Leiva, V., & Aykroyd, R. G. (2017). Birnbaum-Saunders spatial modelling and diagnostics applied to agricultural engineering data. Stoch. Environ. Res. Risk Assess., 31(1), 105–124.
Abstract: Applications of statistical models to describe spatial dependence in geo-referenced data are widespread across many disciplines including the environmental sciences. Most of these applications assume that the data follow a Gaussian distribution. However, in many of them the normality assumption, and even a more general assumption of symmetry, are not appropriate. In non-spatial applications, where the data are uni-modal and positively skewed, the Birnbaum-Saunders (BS) distribution has excelled. This paper proposes a spatial log-linear model based on the BS distribution. Model parameters are estimated using the maximum likelihood method. Local influence diagnostics are derived to assess the sensitivity of the estimators to perturbations in the response variable. As illustration, the proposed model and its diagnostics are used to analyse a real-world agricultural data set, where the spatial variability of phosphorus concentration in the soil is considered-which is extremely important for agricultural management.
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Girard, A., Gago, E. J., Muneer, T., & Caceres, G. (2015). Higher ground source heat pump COP in a residential building through the use of solar thermal collectors. Renew. Energy, 80, 26–39.
Abstract: This article investigates the feasibility of achieving higher performance from ground-source heat-pumps (GSHP) in space heating mode through the use of solar thermal collectors. A novel simulation tool for solar-assisted ground-source heat-pumps (SGSHP) is presented with an analysis of the influence of solar collectors on the improvement of heat pump performance. Solar radiation and climate temperature data of 19 European cities were used to perform simulations of SGSHP and GSHP systems considering a typical residential house. Overall performance coefficients (COPsys) varied from northern to southern locations between 4.4 and 5.8 for SGSHP and between 4.3 and 5.1 for GSHP. Results show that solar collectors coupling has more impact on performance improvement in regions that benefit from higher irradiance. However, greater running cost savings are achieved in milder climate conditions. Both heat-pump systems are able to effectively contribute to carbon footprint reductions for residential buildings, especially in countries where fossil fuels are the primary source of electricity generation. SGSHP payback periods are found between 8.5 and 23 years from northern to southern localities, making such heating system an economic heating option. SGSHPs are best suited for high irradiance and cool climate locations such as the mountainous regions in southern Europe. (C) 2015 Elsevier Ltd. All rights reserved.
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Girard, A., Muneer, T., & Caceres, G. (2014). A validated design simulation tool for passive solar space heating: Results from a monitored house in West Lothian, Scotland. Indoor Built Environ., 23(3), 353–372.
Abstract: Determining the availability of renewable sources on a particular site would result in increasing the efficiency of buildings through appropriate design. The overall aim of the project is to develop a pioneering software tool allowing the assessment of possible energy sources for any building design project. The package would allow the user to simulate the efficiency of the Passive Solar Space Heating referred in the Low and Zero Carbon Energy Sources (LZCES) Strategic Guide stated by the Office of the Deputy Prime Minister (2006) and the Building Regulations. This research paper presents the tool for modelling the passive solar sources availability in relation to low-carbon building. A 3-month experimental set up monitoring a solar house in West Lothian, Scotland, was also undertaken to validate the simulation tool. Experimental and simulation results were found in good agreement following a one-to-one relationship demonstrating the ability of the newly developed tool to assess potential solar gain available for buildings. This modelling tool is highly valuable in consideration of the part L of the Building Regulations (updated in 2010).
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Lagos, R., Canessa, E., & Chaigneau, S. E. (2019). Modeling stereotypes and negative self-stereotypes as a function of interactions among groups with power asymmetries. J. Theory Soc. Behav., 49(3), 312–333.
Abstract: Stereotypes is one of the most researched topics in social psychology. Within this context, negative self-stereotypes pose a particular challenge for theories. In the current work, we propose a model that suggests that negative self-stereotypes can theoretically be accounted for by the need to communicate in a social system made up by groups with unequal power. Because our theory is dynamic, probabilistic, and interactionist, we use a computational simulation technique to show that the proposed model is able to reproduce the phenomenon of interest, to provide novel accounts of related phenomena, and to suggest novel empirical predictions. We describe our computational model, our variables' dynamic behavior and interactions, and link our analyses to the literature on stereotypes and self-stereotypes, the stability of stereotypes (in particular, gender and racial stereotypes), the effects of power asymmetries, and the effects of intergroup contact.
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Leiva, V., Ferreira, M., Gomes, M. I., & Lillo, C. (2016). Extreme value Birnbaum-Saunders regression models applied to environmental data. Stoch. Environ. Res. Risk Assess., 30(3), 1045–1058.
Abstract: Extreme value models are widely used in different areas. The Birnbaum-Saunders distribution is receiving considerable attention due to its physical arguments and its good properties. We propose a methodology based on extreme value Birnbaum-Saunders regression models, which includes model formulation, estimation, inference and checking. We further conduct a simulation study for evaluating its performance. A statistical analysis with real-world extreme value environmental data using the methodology is provided as illustration.
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Leiva, V., Marchant, C., Ruggeri, F., & Saulo, H. (2015). A criterion for environmental assessment using Birnbaum-Saunders attribute control charts. Environmetrics, 26(7), 463–476.
Abstract: Assessing environmental risk is useful for preventing adverse effects on human health in highly polluted cities. We design a criterion for environmental monitoring based on an attribute control chart for the number of dangerous contaminant levels when the concentration to be monitored follows a Birnbaum-Saunders distribution. This distribution is being widely applied to environmental data. We provide a novel justification for its usage in environmental sciences. The control coefficient and the minimum inspection concentration for the designed criterion are determined to yield the specified in-control average run length, whereas the out-of-control case is obtained according to a shift in the target mean. A simulation study is conducted to evaluate the proposed criterion, which reports its performance to provide earlier alerts of out-of-control processes. An application with real-world environmental data is carried out to validate its coherence with what is reported by the health authority. Copyright (c) 2015 John Wiley & Sons, Ltd.
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Leiva, V., Santos-Neto, M., Cysneiros, F. J. A., & Barros, M. (2016). A methodology for stochastic inventory models based on a zero-adjusted Birnbaum-Saunders distribution. Appl. Stoch. Models. Bus. Ind., 32(1), 74–89.
Abstract: The Birnbaum-Saunders (BS) distribution is receiving considerable attention. We propose a methodology for inventory logistics that allows demand data with zeros to be modeled by means of a new discrete-continuous mixture distribution, which is constructed by using a probability mass at zero and a continuous component related to the BS distribution. We obtain some properties of the new mixture distribution and conduct a simulation study to evaluate the performance of the estimators of its parameters. The methodology for stochastic inventory models considers also financial indicators. We illustrate the proposed methodology with two real-world demand data sets. It shows its potential, highlighting the convenience of using it by improving the contribution margins of a Chilean food industry. Copyright (c) 2015 John Wiley & Sons, Ltd.
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Leiva, V., Saulo, H., Leao, J., & Marchant, C. (2014). A family of autoregressive conditional duration models applied to financial data. Comput. Stat. Data Anal., 79, 175–191.
Abstract: The Birnbaum-Saunders distribution is receiving considerable attention due to its good properties. One of its extensions is the class of scale-mixture Birnbaum-Saunders (SBS) distributions, which shares its good properties, but it also has further properties. The autoregressive conditional duration models are the primary family used for analyzing high-frequency financial data. We propose a methodology based on SBS autoregressive conditional duration models, which includes in-sample inference, goodness-of-fit and out-of-sample forecast techniques. We carry out a Monte Carlo study to evaluate its performance and assess its practical usefulness with real-world data of financial transactions from the New York stock exchange. (C) 2014 Elsevier B.V. All rights reserved.
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Lillo, C., Leiva, V., Nicolis, O., & Aykroyd, R. G. (2018). L-moments of the Birnbaum-Saunders distribution and its extreme value version: estimation, goodness of fit and application to earthquake data. J. Appl. Stat., 45(2), 187–209.
Abstract: Understanding patterns in the frequency of extreme natural events, such as earthquakes, is important as it helps in the prediction of their future occurrence and hence provides better civil protection. Distributions describing these events are known to be heavy tailed and positive skew making standard distributions unsuitable for modelling the frequency of such events. The Birnbaum-Saunders distribution and its extreme value version have been widely studied and applied due to their attractive properties. We derive L-moment equations for these distributions and propose novel methods for parameter estimation, goodness-of-fit assessment and model selection. A simulation study is conducted to evaluate the performance of the L-moment estimators, which is compared to that of the maximum likelihood estimators, demonstrating the superiority of the proposed methods. To illustrate these methods in a practical application, a data analysis of real-world earthquake magnitudes, obtained from the global centroid moment tensor catalogue during 1962-2015, is carried out. This application identifies the extreme value Birnbaum-Saunders distribution as a better model than classic extreme value distributions for describing seismic events.
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Marchant, C., Leiva, V., & Cysneiros, F. J. A. (2016). A Multivariate Log-Linear Model for Birnbaum-Saunders Distributions. IEEE Trans. Reliab., 65(2), 816–827.
Abstract: Univariate Birnbaum-Saunders models have been widely applied to fatigue studies. Calculation of fatigue life is of great importance in determining the reliability of materials. We propose and derive new multivariate generalized Birnbaum-Saunders regression models. We use the maximum likelihood method and the EM algorithm to estimate their parameters. We carry out a simulation study to evaluate the performance of the corresponding maximum likelihood estimators. We illustrate the new models with real-world multivariate fatigue data.
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